Are Ontologies Trees or Lattices?

Ontologies, it is sometimes said, take the form of a hierarchy or tree: each class is subdivided into distinct subclasses with no cross classifications. But if the purpose of an ontology is to make possible useful inferences and to guide software users and developers, it is better to allow a more flexible structure. Using text annotation as an example (with concrete reference to the CATMA annotation tool), we argue that it will be more useful to structure ontologies as lattices, not trees.